Multiply the following complex numbers: $({1-3i}) \cdot ({-3-i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({1-3i}) \cdot ({-3-i}) = $ $ ({1} \cdot {-3}) + ({1} \cdot {-1}i) + ({-3}i \cdot {-3}) + ({-3}i \cdot {-1}i) $ Then simplify the terms: $ (-3) + (-1i) + (9i) + (3 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -3 + (-1 + 9)i + 3i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -3 + (-1 + 9)i - 3 $ The result is simplified: $ (-3 - 3) + (8i) = -6+8i $